Papers by Mikkel Willum Johansen
Synthese, Nov 28, 2018
Mathematicians' use of external representations constitutes an important focal point in current p... more Mathematicians' use of external representations constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and cognitive semantics as well as the broader theory of cognitive integration as an analytical lens. We conclude that research mathematicians engage in generative feedback loops with material representations, that they use representations to facilitate the use of experiences of handling the physical world as a resource in mathematical work, and that their use of representations is socially sanctioned and enabled. These results verify the validity of the cognitive frameworks used as the basis for our analysis, but also show the need for augmentation and revision. Especially, we conclude that the social and cultural context cannot be excluded from cognitive analysis of mathematicians' use of external representations. Rather, representations are socially sanctioned and enabled in an enculturation process.
Cognitive Semiotics, Mar 26, 2018
Based on semiotic analyses of examples from the history of mathematics, we claim that the influen... more Based on semiotic analyses of examples from the history of mathematics, we claim that the influence of the material aspects of diagram tokens is anything but trivial. We offer an interpretation of examples of diagrammatic reasoning processes in mathematics according to which the mathematical ideas, arguments, and concepts in question are shaped by the physical features of the chosen diagram tokens.
Lecture Notes in Computer Science, 2022
International Journal for Educational Integrity
Plagiarism and other transgressions of the norms of academic integrity appear to be a persistent ... more Plagiarism and other transgressions of the norms of academic integrity appear to be a persistent problem among upper secondary students. Numerous surveys have revealed high levels of infringement of what appear to be clearly stated rules. Less attention has been given to students’ understanding of academic integrity, and to the potential misconceptions and false beliefs that may make it difficult for them to comply with existing rules and handle complex real-life situations.In this paper we report findings from a survey of European upper secondary students’ views on issues relating to academic integrity. We relate these findings to the students’ training about academic integrity, self-reported level of questionable behavior and country of study.A total of 1654 students at 51 institutions located in 6 European countries participated in the study. The participants generally believed they had a good understanding of the rules applying to them and knew how to behave in compliance with n...
Eksperimenter går ikke altid, som man regner med. Ting går galt, og man får maerkelige resultater... more Eksperimenter går ikke altid, som man regner med. Ting går galt, og man får maerkelige resultater-men hvad betyder det for videnskabens metode?
Matematiske modeller er et uundvaerligt redskab, når matematik skal bruges til at beskrive verden... more Matematiske modeller er et uundvaerligt redskab, når matematik skal bruges til at beskrive verden. Men konstruktionen af modeller fører ofte til en raekke videnskabsteoretiske spørgsmål. Forfatterne Din elev følger en af vores ingeniørstuderende gennem en hel dag, deltager i undervisningen og i projektarbejdet. Eleven får en rundvisning på Det Tekniske Fakultet, ser laboratorier og vores andre spaendende, innovative faciliteter. Dagen giver et indblik i at studere på ingeniøruddannelserne, og eleven får mulighed for at spørge vores studerende om alt fra det faglige til det sociale. Målet er at give dine elever forudsaetningerne for at tage et kvalificeret studievalg. Vores studievejleder står ligeledes til rådighed på dagen. Eleven laver selv besøgsaftalen. Studerende for en dag afholdes i februar-maj og september-december. Mere information og tilmelding: www.sdu.dk/tek/studerendeforendag Find vores forskellige ingeniøruddannelser på: www.sdu.dk/ing
Mathematics, Education and History, 2018
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Diagrammatic Representation and Inference, 2020
The role and use of diagrams in mathematical research has recently attracted increasing attention... more The role and use of diagrams in mathematical research has recently attracted increasing attention within the philosophy of mathematics, leading to a number of in-depth case studies of how diagrams are used in mathematical practice. Though highly interesting, the study of diagrams still largely lack quantitative investigations which can provide vital background information regarding variations e.g. in the frequency or type of diagrams used in mathematics publication over time. A first attempt at providing such quantitative background information has recently been conducted [9], making it clear that the manual labour required to identify and code diagrams constitutes a major limiting factor in large-scale investigations of diagram-use in mathematics. In order to overcome this limiting factor, we have developed a machine learning tool that is able to identify and count mathematical diagrams in large corpora of mathematics texts. In this paper we report on our experiences with this first attempt to bring machine learning tools to the aid of philosophy of mathematics. We describe how we developed the tool, the choices we made along the way, and how reliable the tool is in identifying mathematical diagrams in corpora outside of its training set. On the basis of these experiences we discuss how machine learning tools can be used to inform philosophical discussions, and we provide some ideas to new and valuable research questions that these novel tools may help answer.
The use of computer technology for teaching and learning of mathematics has several consequences ... more The use of computer technology for teaching and learning of mathematics has several consequences and does sometimes give rise to both controversies and misunderstandings. We address these problems by both a philosophical and a historical approach, investigating what it actually is that goes on when new technologies enter mathematics as a discipline and mathematics education as a societal practice. Our analysis suggests a focus on continuities in time and place in the sense that it is necessary to understand the history of “tool use” in mathematics and the various ways that scholastic and non-scholastic mathematical practices adopt such tools. Furthermore we point to the strong interrelation between mathematics as a body of knowledge, mathematical activity and the technologies used for mathematical work. Finally we discuss how different theoretical lenses and epistemological outsets give rise to different guidelines and conclusions regarding the use of computer technology in mathemat...
Anmeldelse af Maria Kirstine Ostergaard: “Matematikangst – fordomme og kon”. Frydenlund, 2018, 11... more Anmeldelse af Maria Kirstine Ostergaard: “Matematikangst – fordomme og kon”. Frydenlund, 2018, 114 sider.
European Journal for Philosophy of Science, 2021
Accountability in Research, 2020
Johansen (2020): Good friend or good student? An interview study of perceived conflicts between p... more Johansen (2020): Good friend or good student? An interview study of perceived conflicts between personal and academic integrity among students in three European countries, Accountability in Research,
Science and Engineering Ethics, 2020
This paper presents and discusses empirical results from a survey about the research practice of ... more This paper presents and discusses empirical results from a survey about the research practice of Danish chemistry students, with a main focus on the question of anomalous data. It seeks to investigate how such data is handled by students, with special attention to so-called ‘questionable research practices’ (QRPs) where anomalous data are simply deleted or discarded. This question of QRPs is of particular importance as the educational practices students experience may influence how they act in their future professional careers, for instance in research. The ethical evaluation of QRPs however is not univocal. In parts of the literature QRPs are seen as unquestionably bad, while in other parts of the literature certain QRPs are seen as a necessary aspect of scientific practice. Results from the survey of Danish chemistry students shows that many students engage in certain types of questionable practices, and that a large minority of the students have been actively encouraged by their teachers to engage in such practices. The paper discusses to what extent and under what circumstances such instructional practices can be defended and suggests how the instructional practice connected to the handling of anomalous data can be improved.
Synthese, 2019
We present a case study of how mathematicians write for mathematicians. We have conducted intervi... more We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam's very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors' purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.
Synthese, 2018
Mathematicians' use of external representations constitutes an important focal point in current p... more Mathematicians' use of external representations constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and cognitive semantics as well as the broader theory of cognitive integration as an analytical lens. We conclude that research mathematicians engage in generative feedback loops with material representations, that they use representations to facilitate the use of experiences of handling the physical world as a resource in mathematical work, and that their use of representations is socially sanctioned and enabled. These results verify the validity of the cognitive frameworks used as the basis for our analysis, but also show the need for augmentation and revision. Especially, we conclude that the social and cultural context cannot be excluded from cognitive analysis of mathematicians' use of external representations. Rather, representations are socially sanctioned and enabled in an enculturation process.
Cognitive Semiotics, 2016
Based on semiotic analyses of examples from the history of mathematics, we claim that the influen... more Based on semiotic analyses of examples from the history of mathematics, we claim that the influence of the material aspects of diagram tokens is anything but trivial. We offer an interpretation of examples of diagrammatic reasoning processes in mathematics according to which the mathematical ideas, arguments, and concepts in question are shaped by the physical features of the chosen diagram tokens.
Uploads
Papers by Mikkel Willum Johansen